Where does relation collide?

In set theory a relation is a set of ordered pairs, that is, any subset of the Cartesian product of two sets, and it records exactly which elements of the first set stand in a given association with which elements of the second. Halmos's 1974 Naive Set Theory defined a relation this way and derived from it the properties a relation may have, such as being reflexive, symmetric, or transitive. The referent here is a pure mathematical object, a collection of pairs with no content of its own, and it is not a stored table of business data, a bond between people, or the role a phrase plays in a clause.[1]

Unit

One ordered pair either belongs or does not; the relation is the whole set of pairs that do

Recovery means

Not applicable

Measured by

Specified by listing its pairs or by a rule that decides, for any pair, whether it is in the set

In Codd's relational model a relation is a table of data: a set of tuples that all share the same named attributes, so each row is one record and each column one attribute drawn from a fixed domain. Codd's 1970 A Relational Model of Data for Large Shared Data Banks proposed organising stored data as such relations so that users could query it without knowing how it is laid out in the machine. This referent is a concrete data structure holding facts about a business or a system, and although Codd built it on the mathematical meaning of a relation, it is not a bare set of pairs, a tie between people, or a grammatical role.[2]

Unit

One relation is one table; one tuple is one row of values over the shared attributes

Recovery means

Not applicable

Measured by

Defined by a schema of attributes, populated with tuples, and read by relational operations and queries

In sociology a social relation is a recurring connection between social actors, such as an exchange, a bond of kinship, or a difference of power, and much of the field treats these connections, rather than individuals or their attributes, as the basic material of social structure. Emirbayer's 1997 Manifesto for a Relational Sociology argued that the link or transaction between actors should be the primary unit of analysis. The referent is a lived connection between people or groups, studied for how it shapes action, and it is not a set of ordered pairs, a stored table, or the role a phrase plays in a sentence.[3]

Unit

One relation is one standing connection between actors, such as a tie of exchange or kinship

Recovery means

Not applicable

Measured by

Traced through fieldwork, surveys, or network data that record who is connected to whom and how

In syntax a grammatical relation is the functional role a phrase plays within its clause, such as subject, direct object, or indirect object, defined by how it behaves rather than by its meaning or its position alone. Keenan and Comrie's 1977 study of noun phrase accessibility treated these relations as primitives ranked on a hierarchy, with the subject the most accessible to operations like relative clause formation. The referent is a structural role a word or phrase occupies in a sentence, and it has nothing to do with a set of ordered pairs, a table of data, or a connection between people.[4]

Unit

One relation is one clause-level role, such as subject or object, borne by a phrase

Recovery means

Not applicable

Measured by

Identified by grammatical tests such as agreement, case marking, and access to syntactic operations